Let f(x)= -2x+4 and g(x)=x²+x-1 what is f(g(2))

To find \( f(g(2)) \), we first need to compute \( g(2) \) and then use that result to find \( f(g(2)) \).

### Step 1: Calculate \( g(2) \)

Given the function \( g(x) = x^2 + x - 1 \), substitute \( x = 2 \):

\[
g(2) = 2^2 + 2 - 1
\]

\[
g(2) = 4 + 2 - 1 = 5
\]

### Step 2: Calculate \( f(g(2)) = f(5) \)

Now we need to use the result of \( g(2) = 5 \) in the function \( f(x) = -2x + 4 \):

\[
f(5) = -2 \cdot 5 + 4
\]

\[
f(5) = -10 + 4 = -6
\]

### Conclusion

\[
f(g(2)) = -6
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is \( g(f(2)) \) for the same functions?
2. Find \( f(g(x)) \) in terms of \( x \).
3. Calculate the value of \( g(g(1)) \).
4. If \( h(x) = x^3 - 2x \), what is \( f(h(1)) \)?
5. Determine the roots of the equation \( f(x) = 0 \).

**Tip:** When solving composite functions, always start from the innermost function and work outward.

Let f(x)= -2x+4 and g(x)=x²+x-1 what is f(g(2))?

Learn how to solve the composite function f(g(2)) where f(x) = -2x + 4 and g(x) = x² + x - 1. This problem demonstrates key algebra concepts, including function composition, quadratic and linear equations. Suitable for students in Grades 8-10.

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