Question

If f(x)=1/3x+7 and g(x)=-2x-5, find f(g(-7)) Please help.

Answer 1

Answer:

$f(g(-7))=10$

Step-by-step explanation:

We have the two functions:

$\displaystyle f(x)=\frac{1}{3}x+7\text{ and } g(x)=-2x-5$

And we want to find:

$f(g(-7))$

So, we will first find g(-7). We know that:

$g(x)=-2x-5$

Then by substitution:

$g(-7)=-2(-7)-5$

Evaluate. Multiply:

$g(-7)=14-5=9$

Therefore, we can rewrite our expression as:

$f(g(-7))=f(9)$

Since we know that:

$\displaystyle f(x)=\frac{1}{3}x+7$

By substitution:

$\displaystyle f(9)=\frac{1}{3}(9)+7$

Evaluate:

$f(9)=3+7=10$

Therefore:

$f(g(-7))=10$

Answer 2

Answer:

$\boxed {\boxed {\sf f(g(-7))= 10}}$

Step-by-step explanation:

We are asked to find f(g(-7)) given these 2 functions:

• $f(x)=\frac{1}{3}x+7$

• $g(x)= -2x-5$

We must work from the inside out, so first find g(-7).

1. g(-7)

The function for g is:

$g(x)= -2x-5$

Since we want to find g(-7), plug -7 in for x.

$g(-7)= -2(-7)-5$

Solve according the PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Multiply -2 and -7.

$g(-7)=14-5$

Subtract 5 from 14.

$g(-7)=9$

2. f(9)

Refer back to the original problem: f(g(-7))

Since we found that g(-7) is 9, we can substitute 9 in: f(9)

The function for f is:

$f(x)= \frac{1}{3} x+7$

Plug 9 in for x.

$f(9)=\frac{1}{3}(9)+7$

Solve according to PEMDAS and multiply 1/3 and 9.

$f(9)=3+7$

Add 3 and 7.

$f(9)=10$

f(g(-7) is equal to 10