Question

If f(x)=2x+1f(x)=2x+1f, left parenthesis, x, right parenthesis, equals, 2, x, plus, 1 and g(x)=x^2+7g(x)=x
2
+7g, left parenthesis, x, right parenthesis, equals, x, squared, plus, 7, which of the following is equal to f(g(x))f(g(x))f, left parenthesis, g, left parenthesis, x, right parenthesis, right parenthesis ?
Choose 1 answer:
x^2+2x+8

Answer 1

The value of the composite function f(g(x)) is 2x^2 + 15

How to evaluate the composite function f(g(x))?

The functions are given as:

f(x) = 2x + 1

g(x) = x^2 + 7

We have the function f(x) to be

f(x) = 2x + 1

Substitute g(x) for x in the equation f(x) = 2x + 1

So, we have

f(g(x)) = 2g(x) + 1

Substitute g(x) = x^2 + 7  in the equation f(g(x)) = 2x + 1

f(g(x)) = 2(x^2 + 7) + 1

Open the brackets

f(g(x)) = 2x^2 + 14 + 1

Evaluate the sum

f(g(x)) = 2x^2 + 15

Hence, the value of the composite function f(g(x)) is 2x^2 + 15

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Complete question

if f(x) = 2x + 1 and g(x) = x^2 + 7

which of the following is equal to f(g(x))