Question

"If `f(2) = 10`, which of the following could be the inverse of `f(x)`? " can someone please explain how you got this so i can do the rest of them?

a. `g(x) = 10x^2 - 2x`

b. `g(x) = 2x^3 - 10x`

c. `g(x) = x^3 + 2`

d. `g(x) = x^2 - 9x - 8`

Answer 1

d.

Explanation:

If `f(2)=10` then `g(10)=2`

Test each of them out:

a: `10*10^2-10*10=900`

b `2*10^3-10*10=1900`

c `10^3-2=998`

d `10^2-9*10-8=2`

d. is the only one that has g(10)=2, thus d. is the answer

Answer 2

d. `g(x) = x^2 -9x -8`

Explanation:

If f(2)=10 , we can say that the inverse of f(x) , say g(x) outputs a value of 2 when 10 is the input , that is g(10)=2.
This is precisely the definition of an inverse function. It undoes or inverses the original function.
You can also think of it as the input and output values switching places.
So we can say g(10)=2. The only option that satisfies this is d)`g(x) = x^2 -9x -8`