Home > Algebra > Function Notation

How do you find #(f+g)(-2)# given #f(x)=x^2-1 and #g(x)=2x-3# and #h(x)=1-4x#?

Answer 1

Hazel Anglin

To find (f+g)(-2), substitute x = -2 into f(x) and g(x), then add the results. (f+g)(-2) = 13.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Genesis Allen

See the entire solution process below:

First,

#(f + g)(x) = f(x) + g(x) = x^2 - 1 + 2x - 3#

We can ignore #h(x)# as it is extraneous information to this problem.

To find #(f + g)(-2)# we need to substitute #color(red)(-2)# for each occurrence of #color(red)(x)# in #(f + g)(x)#:

#(f + g)(color(red)(x)) = color(red)(x)^2 - 1 + 2color(red)(x) - 3# becomes:

#(f + g)(color(red)(-2)) = (color(red)(-2))^2 - 1 + (2 * color(red)(-2)) - 3#

#(f + g)(color(red)(-2)) = 4 - 1 - 4 - 3#

#(f + g)(color(red)(-2)) = -4#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.