Express your answer as a polynomial in standard form.
f, of, x, equals, 2, x, minus, 7
f(x)=
2x−7
g, of, x, equals, 3, x, squared, minus, 5, x, minus, 7
g(x)=
3x 
2
 −5x−7
Find: , f, of, g, of, x
Find: f(g(x))

To find \( f(g(x)) \), we will substitute the expression for \( g(x) \) into the function \( f(x) \).

Given:
- \( f(x) = 2x - 7 \)
- \( g(x) = 3x^2 - 5x - 7 \)

Now, to find \( f(g(x)) \), substitute \( g(x) \) into \( f(x) \):

\[
f(g(x)) = 2(3x^2 - 5x - 7) - 7
\]

Now, distribute the \( 2 \) across the terms inside the parentheses:

\[
f(g(x)) = 2(3x^2) + 2(-5x) + 2(-7) - 7
\]

This simplifies to:

\[
f(g(x)) = 6x^2 - 10x - 14 - 7
\]

Finally, combine like terms:

\[
f(g(x)) = 6x^2 - 10x - 21
\]

So, the polynomial in standard form is:

\[
f(g(x)) = 6x^2 - 10x - 21
\]

Would you like further clarification on any part of this solution?

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Here are 5 related questions you can explore:
1. What is \( g(f(x)) \) for the same functions \( f(x) \) and \( g(x) \)?
2. What is \( f(f(x)) \) for \( f(x) = 2x - 7 \)?
3. How would you find the inverse of \( f(x) = 2x - 7 \)?
4. What is the derivative of \( f(g(x)) \)?
5. Can you find the x-intercepts of \( f(g(x)) \)?

**Tip:** When performing composition of functions, always remember to substitute one function fully into the other, following the order indicated.

Find f(g(x)) where f(x) = 2x - 7 and g(x) = 3x^2 - 5x - 7. Express the answer as a polynomial in standard form.

Learn how to find the composition of functions f(x) = 2x - 7 and g(x) = 3x^2 - 5x - 7. This solution explains how to substitute g(x) into f(x) and simplify the resulting expression to get the polynomial in standard form. This concept is ideal for students in Grades 9-11, covering algebraic functions and polynomial simplification.

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