Question

What is f(g(x)) for x > 5?

Answer 1

f(g(x)) (you plug/substitute g(x) into x)

f(x) = 4x - √x

f(g(x)) = 4(g(x)) - √(g(x)) since g(x) = (x - 5)², you can do:

f(g(x)) = 4(x - 5)² - √(x - 5)² The ² and √ cancel each other, leaving

f(g(x)) = 4(x - 5)² - (x - 5) Next factor out (x - 5)² or (x - 5)(x - 5)

f(g(x)) = 4(x² - 10x + 25) - (x - 5) Now distribute the 4 and the -

f(g(x)) = 4x² - 40x + 100 - x + 5 Simplify

f(g(x)) = 4x² - 41x + 105 Your answer is B

Answer 2

`f(g(x)) =4{x}^(2) - 41x + 105`

Step-by-step explanation

The given functions are:

`f(x) = 4x - √(x)`

and

`g(x) = {(x - 5)}^(2)`

To find

`f(g(x)) = f( {(x - 5)}^(2) )`

`f(g(x)) =4 {(x - 5)}^(2) - \sqrt{{(x - 5)}^(2) }`

We expand and simplify to obtain,

`f(g(x)) =4 {( {x}^(2) - 10x + 25)} - (x - 5)`

`f(g(x)) =4{x}^(2) - 40x + 100 - x + 5`

Combine similar terms to get;

`f(g(x)) =4{x}^(2) - 41x + 105`

The correct choice is B.