Question

In this activity, you'll combine two related functions, f(x) = 6x + 5 and x(y) = 4y2 – 25, to create a type of function called a composite function. Then you’ll evaluate the composite function. For the given functions, find f(x) if y = 3.

Answer 1

x(y) =4y^2 − 25.

So:

x(3) = 4(3)^2 − 25

=36 − 25

=11.

Substituting this value in f(x):

f(x) =

f(11) = 6(11) + 5

f(11) =71.

If y = 3, f(x) = 71.

Answer 2

we are given

`f(x)=6x+5`

`x=4y^2 -25`

we can plug x into f(x)

`f(x)=6(4y^2 -25)+5`

now, we can simplify it

`f(x)=6*4y^2 -6*25+5`

`f(x)=24y^2 -150+5`

`f(x)=24y^2 -145`

now, we can plug y=3

`f(x)=24(3)^2 -145`

`f(x)=71`.............................Answer