Use the variable u for the inside function to express each of the following as a composite function. (a) y=(5 t²-3) NOTE: u(t) is the inside function and y(u) is the outside function. u(t) =

Q: The percentage y (of total personal consumption) an individual spends on food is approximately y =…

A: Directly substitute the expression of X and simplify. For percentage change take the derivative and…

Q: 9. Use the product rule to find and state the rule for dif- ferentiating a product of three…

A: The product rule of differentiation is given by,…

Q: Consider the function y = (1x + 1)x. (a) Differentiate y by the product rule. (b) First, multiply…

A: (a) Differentiate y by the product rule as follows: dydx=ddxx+1x      =ddxx+1x+ddxxx+1      =1·…

Q: Find the inverse of the function f (x)= \x-2.

A: To find the inverse of the function,  Let y=f(x) Therefore, x=f-1(y) Substitute y in place of f(x)…

Q: Write the height h of the rectangle as a function of x.

A: In two-dimension cartesian-coordinate system, the value of a function at a point represented by the…

Q: An exponentional function takes the form y= ab x . What does the "a", and "b" represent?

A: solution:-

Q: A scientist observed that the speed S at which certain ants ran was a function of T, the ambient…

A:

Q: Let f(x) = 3x? +x - 5. Evaluate each function value. (b) f(0) (a) f(-2) (c) f(4) (d) f(;)

A: Given function is fx=3x2+x-5. (a) To find f-2. Solution: We have fx=3x2+x-5. Put x=-2…

Q: What type of discontinuity does the function f(x)=xsecx have?

A:

Q: Find f if f"(x) = 4 – 6x, f(0) = 3, and f(2) = -2. %3D Answer: f(æ)

A:

Q: R(x) = //x – 1 X.

A:

Q: 3* f(x) =

A: Let I denote the open interval (a, b) in R and let x0∈I. Then a function f: I→R is said to be…

Q: f(u) = u + 1 h(u) : Vu + 1 p(u) = 1 - 4u2 q(u) = (1 – 4u2)9 g(u) = Vu + 1(1 – 4u2)9

A: Given functions are,