1. Let A = {r E R : e # 2} and define f : A R by f(x) = . 5r+1 I-2 (a) Show thatf is one-to-one. (b) Show that if y + 5, then y E rng f. (c) Show that 5 ¢ rng f.

Q: (8) 3a. Given the functions f(x) and g(x), find: a) domain b) range c) inverse of the function d)…

A:

Q: If f(x)= [2 x] then f(-2.1)= O a) -5/ b) -4.2 c) -6 d) -7 Oe) None of the above.

A: Ans:- (a) -5  For detail...go through the solution...I have solved in detail

Q: 26. Which restriction would enable the function )= x+ ór- 9 to have an inverse function? A. 12 9 3…

A: Find the roots of the polynomial then check one one domain

Q: Find the values of a such that det (² 3-x 2 3-x 4 1 -1 -1-x = 0.

A: We have to find the value of x such thatWe know that

Q: (d) Operator -iħd/dx and function exp(-ikx). (e) Operator -ħ?d?/dx² and function exp(-ikx).

A:

Q: 2. Consider the functions g, h: R → R defined by g(x) = x² and h(x) = x³ + 1. A. Evaluate f(g(x) ·…

A: g(x)=x2h(x)=x3+1∫xndx=xn+1n+1+c

Q: X+2 If f(x)= for which of the following X-1 values of xis ((x) undefined? A) -2 B) -1 1 C) D) 1

A: The given function is  f(x) = (x + 2)/(x - 1)

Q: Use the table below to fill in the missing values. Assume f(x) is a one-to-one functi f(x) 7 0 2 3 1…

A: A table is given with a one to one function fx values for some values of x. a) The objective is to…

Q: Derive the autocorrelation function of: x₁ = $xt-1 + εt + 0€t-1 assuming that p < 1, and E(?) = 0²,…

A:

Q: 2. Functions f and g are defined as follows: f:R -R f(x) = x2 – 3x –1 Perform these expressions…

A:

Q: of Əf Find and дх ду Əf дх — II for the following function. f(x,y) = (5x – 2y)5

A:

Q: (f*g) o F. y. Let f and g be two multiplicative functions and ES. We have fo (goF)

A:

Q: Let n be a positive integer. Define the function fn(z) by dn dzn Find the value of fn(-1+i).…

A: Solution:Given: Let be a positive integer. the function is defined bywe have to find the value of

Q: My friend told me that negative exponents "sometimes" inverse the fraction (i.e  X-2 +2 / 5 = 5/ x-2…

A: A negative exponent is solved by taking the multiplicative inverse of the base raise to the positive…

Q: Find the inverse of the relation Express your answer in terms of the new 'y'. (x+7)²+(y-6)² = 19

A:

Q: Find graphically approximate value of the root of the equation an 3 – x = e* - 1.

A:

Q: 3. Let f : A → B. Then 18f = f and f1a = f. Hint. You may use the fact that fg, for functions f, g,…

A:

Q: Consider the table of values for the function f(x). X 1 2 W|N 3 4 a) 3 b) 4 O c) 1 y = f(x) 3 1 What…

A: Given query is to find individual function.

Q: EX:- Find the F.I. of (f(t)) sgn (t) =

A: ft= sgntft=1if x&gt;00if x=0-1if x&lt;0 The signum function can also be represented as…

Q: (0,-6) (1,-7) ssuming that f(x) is of the form A. Bº, write an xpression for f(x): (x) = 0

A: Given query is to find indicated function.

Q: Given a function, 2, xeR. Find the inverse function for f(x) D, mR. m{ ne, wo) AND R, mD -a. ) and…

A: Use rule to find inverse function

Q: Find the inverse of each function. 5) flx) = -2x +3

A:

Q: The figure defines a function f from A={r, s, t, u} into B={a, b, c, d} in the obvious way. Which of…

A:

Q: Assume that the relation x = √500+ 5y² defines y implicitly as a function of x. Determine y" as a…

A:

Q: 2) a. Find the inverse of the function, b. Show that the function f: R> R defined as f (x) = 13x –…

A:

Q: Use the function f(r) given below to answer the questions that follow. f(r) = – 2(r+1)(r – 3) (r –…

A: The given function f(r)=-2r+1r-33(r-1)

Q: Q1 a) let f be a function defined as f(x)=3x² + 2x². Find f(2), f(-1), f(1). b) Define functions f…

A:

Q: - Let f(x) = 3* a) What is f(x) ? c) Use the table from b) to complete the table for the inverse…

A:

Q: Let f (x) = x + 6 and g (a) = Vx – 6. Find rules for fog and go f to show that f and g are inverses.

A: