High School

Given the following functions [tex]f(x)[/tex] and [tex]g(x)[/tex], solve for [tex]f(g(7))[/tex].

[tex]\begin{array}{l} f(x) = 4x + 21 \\ g(x) = 2x + 2 \end{array}[/tex]

A. 16
B. 49
C. 85
D. 784

Answer :

To solve the problem of finding [tex]\(f(g(7))\)[/tex], you need to follow these steps:

1. Identify the given functions:
- [tex]\( f(x) = 4x + 21 \)[/tex]
- [tex]\( g(x) = 2x + 2 \)[/tex]

2. Calculate [tex]\(g(7)\)[/tex]:
- Substitute [tex]\(x = 7\)[/tex] into the function [tex]\(g(x)\)[/tex].
- [tex]\( g(7) = 2(7) + 2 \)[/tex]
- [tex]\( g(7) = 14 + 2 \)[/tex]
- [tex]\( g(7) = 16 \)[/tex]

3. Calculate [tex]\(f(g(7))\)[/tex] or [tex]\(f(16)\)[/tex]:
- Now use the result from the previous step in the function [tex]\(f(x)\)[/tex].
- Substitute [tex]\(16\)[/tex] into the function [tex]\(f(x)\)[/tex].
- [tex]\( f(16) = 4(16) + 21 \)[/tex]
- [tex]\( f(16) = 64 + 21 \)[/tex]
- [tex]\( f(16) = 85 \)[/tex]

Thus, the value of [tex]\(f(g(7))\)[/tex] is [tex]\(85\)[/tex].

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