Question

Evaluate the function f(x) = x² + 3x - 2 at the given values of the independent variable and simplify.a. f(-1)b. f(x+5)c. f(-x)a. f(-1)=(Simplify your answer.)b. f(x+5)=(Simplify your answer.)c. f(-x) = (Simplify your answer.)

Answer 1

Given:

f(x) = x^2 + 3x - 2

(a) f(-1)

lets substitute x = -1 to the given equation.

f(x) = x^2 + 3x - 2

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

= 1 - 3 - 2

= -4

(b) f(x+5)

lets substitute x + 5 to the given equation.

f(x) = x^2 + 3x - 2

f(x+5) = (x + 5)^2 + 3(x + 5) - 2

= (x^2 + 5x + 5x + 25) + 3x + 15 - 2

= x^2 + 10x + 25 + 3x + 15 - 2

= x^2 + 13x + 38

(c) f(-x)

lets substitute x-----> -x to the given equation.

f(x) = x^2 + 3x - 2

f(-x) = (-x)^2 + 3(-x) - 2

= x^2 - 3x - 2

Therefore the corresponding answers are:

f(-1) = -4

f(x + 5) = x^2 + 13x + 38

f(-x) = x^2 - 3x - 2