Question

Evaluate ( f(c-5) ) when ( f(x) = -2x - 3 ).

a) ( -2c - 13 )

b) ( 2c - 7 )

c) ( -2c + 13 )

d) ( 2c + 7 )

Answer 1

To find f(c-5) for the function f(x)=-2x-3, substitute c-5 for x, leading to the expression -2(c-5)-3, which simplifies to -2c+7, matching option d.

Step-by-step explanation:

To evaluate ( f(c-5) ) when ( f(x) = -2x - 3 ), we need to substitute (c-5) into the given function for x. Here's how it's done step by step:

1. Start with the original function: f(x) = -2x - 3.
2. Replace every instance of x with (c-5): f(c-5) = -2(c-5) - 3.
3. Distribute the -2 across (c-5): -2c + 10 - 3.
4. Combine like terms: -2c + 7.

The correct evaluation of ( f(c-5) ) is ( -2c + 7 ), which corresponds to option d.