Question

Use the functions to answer the question.

f(x) = 2x2 – 5x – 3

g(x) = x2 + 6x – 1

What is h(x) if h(x) = g(x) - f(x)?

Answer 1

`h(x) = -x^2+11x+2`

Explanation:

`f(x) = 2x^2 - 5x -3\\g(x) = x^2 + 6x -1`

As the question is saying
`h(x) = g(x) - f(x)`, we need to substitute the values of
`g(x)` and
`f(x)` into this equation to solve for
`h(x)`.

Substitute the values of g(x) and f(x) into the h(x) equation:

`h(x) = x^2+6x-1 -(2x^2-5x-3)`

Distribute the negative sign into the expression for f(x):

`h(x) = x^2+6x-1-2x^2+5x+3`

Add the like terms (terms with the same variable and same exponent) to simplify:

⭐
`x^2-2x^2 = -x^2`

⭐
`6x+5x = 11x`

⭐
`-1+3 = 2`

∴
`h(x) = -x^2+11x+2`