Respuesta :

xKelvin

Answer:

[tex]f(g(-7))=10[/tex]

Step-by-step explanation:

We have the two functions:

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

And we want to find:

[tex]f(g(-7))[/tex]

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

[tex]g(x)=-2x-5[/tex]

Then by substitution:

[tex]g(-7)=-2(-7)-5[/tex]

Evaluate. Multiply:

[tex]g(-7)=14-5=9[/tex]

Therefore, we can rewrite our expression as:

[tex]f(g(-7))=f(9)[/tex]

Since we know that:

[tex]\displaystyle f(x)=\frac{1}{3}x+7[/tex]

By substitution:

[tex]\displaystyle f(9)=\frac{1}{3}(9)+7[/tex]

Evaluate:

[tex]f(9)=3+7=10[/tex]

Therefore:

[tex]f(g(-7))=10[/tex]

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf f(g(-7))= 10}}[/tex]

Step-by-step explanation:

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

  • [tex]f(x)=\frac{1}{3}x+7[/tex]
  • [tex]g(x)= -2x-5[/tex]

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

1. g(-7)

The function for g is:

[tex]g(x)= -2x-5[/tex]

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

[tex]g(-7)= -2(-7)-5[/tex]

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

Multiply -2 and -7.

[tex]g(-7)=14-5[/tex]

Subtract 5 from 14.

[tex]g(-7)=9[/tex]

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:

[tex]f(x)= \frac{1}{3} x+7[/tex]

Plug 9 in for x.

[tex]f(9)=\frac{1}{3}(9)+7[/tex]

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

[tex]f(9)=3+7[/tex]

Add 3 and 7.

[tex]f(9)=10[/tex]

f(g(-7) is equal to 10

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