Question

If f(x)=3x-2 and g(x)=x^2+1, find f(g(-1)) and g(f(3))

Answer 1

If f(x)=3x-2 and g(x)=
`x^2+1`, f(g(-1)) = 4, g(f(3)) = 50

Let's find those function values:

f(g(-1)):

First, find g(-1): g(-1) =
`(-1)^2 + 1 = 2.`

Now, plug g(-1) into f(x): f(g(-1)) = f(2) = 3(2) - 2 = 4.

g(f(3)):

First, find f(3): f(3) = 3(3) - 2 = 7.

Now, plug f(3) into g(x): g(f(3)) = g(7) =
`7^2 + 1 = 50.`

Therefore:

f(g(-1)) = 4

g(f(3)) = 50

Answer 2

`f(g(-1))=4`

`g(f(3))=50`

Explanation:

We know the definition of both functions:
`f(x)=3x-2`, and
`g(x)=x^2+1`

A) In order to evaluate what
`f(g(-1)) is`, let's first investigate what g(-1) is using the definition for this function:

`g(x)=x^2+1\\g(-1)=(-1)^2+1\\g(-1)=1+1\\g(-1)=2`

Now let's find what f(2) is using f(x) definition:
`f(x)=3x-2\\f(2)=3(2)-2\\f(2)=6-2\\f(2)=4`

B) In order to evaluate what
`g(f(3)) is`, let's first investigate what f(3) is using the definition for this function:

`f(x)=3x-2\\f(3)=3(3)-2\\f(3)=9-2\\f(3)=7`

Now let's find what g(7) is using the definition for this function:

`g(x)=x^2+1\\g(7)=(7)^2+1\\g(7)=49+1\\g(7)=50`