41. Suppose that both f and g have inverses and that h(x) = (f o g)(x) = f(g(x)). Show that h has an inverse given by h- = gl of-1

Q: Show that f(x) = (3x - 2) / (5x - 3) , is its own inverse ?

A:

Q: 3. (a) Which of the following functions have 5 in their domain? f(x) = x² - 3x *- 5 h(x) = Vx - 10…

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Q: 13. (a) Find the inverse of the functio x) = 2x – 5 (b) Find f- (3)

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Q: Find the inverse of f(x)=1/(x-3)

A: This can be done as follows:

Q: If f(x) = x2 - x/ x - 1 and g(x) = x Is it true that f=g?

A: given  f(x)=x2-xx-1g(x)=x

Q: 2х f(x) = (1 – x²)² a. Express f(x) as a power series. b. Determine the sum of 2n=1-I° 4n- c. Find…

A: The given function is: f(x)=2x(1-x2)2

Q: 3. Two functions are inverses when f(g(x)) = Determine if f(x) = In(x - 5) your work and explain…

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Q: 5. Simplify the difference quotient f(a+h)-f(a) for the function f(x)%3D 3x+4 Use %3D h correct…

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Q: Determine the new value of the function f(x) =x+ Inx if the independent changes from x=2e to x=2.2e

A: Given f(x) = x + ln(x)Value of function at x = 2ef(2e) = 2e + ln(2e) = 2e+1+ln2

Q: 10. What is the inverse of f(x) = 2x + 5? O A.-5 B. 5-2x C. -2 D.

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Q: 7. Find the inverse of f(x) =D5x + 10.

A: y=f(x) iimplise x=f^(-1) (y) given function Find value of x  then replace y  in x

Q: vertical asymptote(s): horizontal asymptote(s):

A: Since multiple subparts are asked, I am answering first 3 subparts

Q: 5. If f(x) = (r+ 1)(x-2) x-2 and g(x) = x+1, does f(x) = g(r)? Explain.

A:

Q: Find f"(x) if f(x) = = 25 x-4 70 (x − 4)²

A: We need to calculate f''(x) for the given function f(x). This can be evaluated as follows:

Q: 10) Find (¹) (3) if f(x)=x²+x-1.

A:

Q: (*-2)*xd 10. Evaluate xdx 1

A: We have to evaluate ∫12(x2-2)4xdx It is solved by using substitution method, Let…

Q: 20) What is the inverse of the function 4y= 2x-8 ?

A: We have to find function

Q: Let f(x) = x^5+x^3+2x, and let g(x) be the inverse of f.

A: Given that,f(x) = x5 + x3 + 2xand g(x) is the inverse of f(x).