Question

f(x)=3x+5
g(x)=4^2-2
h(x)=x^2-3x+1
find f(x)=g(x)-h(x)
a)5x^2+4
b)-5x^2+6
c)-5x^2+6x+6
d)5x^2+6x+4

Answer 1

To find \( f(x) = g(x) - h(x) \), we first need to calculate \( g(x) \) and \( h(x) \).

1. **Calculate \( g(x) \)**:
\[
g(x) = 4^2 - 2 = 16 - 2 = 14
\]
Since \( g(x) \) is a constant value of 14 for all \( x \).

2. **Calculate \( h(x) \)**:
\[
h(x) = x^2 - 3x + 1
\]

3. **Substituting \( g(x) \) and \( h(x) \) into the equation**:
\[
f(x) = g(x) - h(x) = 14 - (x^2 - 3x + 1)
\]

Now, simplifying this:
\[
f(x) = 14 - x^2 + 3x - 1
\]
\[
f(x) = -x^2 + 3x + 13
\]

Now, let’s look for the options provided:
a) \( 5x^2 + 4 \)
b) \( -5x^2 + 6 \)
c) \( -5x^2 + 6x + 6 \)
d) \( 5x^2 + 6x + 4 \)

None of the provided options match \( f(x) = -x^2 + 3x + 13 \). It seems like the function might have been calculated incorrectly, or the options don't correctly represent the functions involved here.

The value derived for \( f(x) \) stands at:
\[
f(x) = -x^2 + 3x + 13
\]

Hence, based on the function relationship and calculations shown above, none of the options clearly represents the computed \( f(x) \).

If you were looking for \( f(x) \) in a different context or wanted any changes to the definition, please clarify for further assistance!