EVALUATE FUNCTION WITH INDICATED INDEPENDENT VARIABLE AND SIMPLIFY

Evaluate the function at the given value of the independent variable and simplify.

Problem 1 :

When f(x) = x² - 5 evaluate f(x - 4)

Solution:

f(x) = x² - 5

f(x - 4) = (x - 4)² - 5

= x² + 16 - 8x - 5

f(x - 4) = x² - 8x + 11

Evaluate each function.

Problem 2 :

When p(a) = -4a - 2; Find p(2a)

Solution:

p(a) = -4a - 2

p(2a) = -4(2a) - 2

= -8a - 2

Problem 3 :

When f(x) = 2x - 4; Find f(x + 3)

Solution:

f(x) = 2x - 4

f(x + 3) = 2(x + 3) - 4

= 2x + 6 - 4

f(x + 3) = 2x + 2

Problem 4 :

When h(n) = 2n - 4; Find h(1 + n)

Solution:

h(n) = 2n - 4

h(1 + n) = 2(1 + n) - 4

= 2 + 2n - 4

h(1 + n) = 2n - 2

Problem 5 :

When f(x) = 4x - 5; Find f(2 + x)

Solution:

f(x) = 4x - 5

f(2 + x) = 4(2 + x) - 5

= 8 + 4x - 5

f(2 + x) = 4x + 3

Problem 6 :

When g(x) = 3x - 2; Find g(2x)

Solution:

g(x) = 3x - 2

g(2x) = 3(2x) - 2

= 6x - 2

Problem 7 :

When h(n) = n + 1; Find h(n + 2)

Solution:

h(n) = n + 1

h(n + 2) = (n + 2) + 1

= n + 3

Problem 8 :

When f(x) = 4x + 4; Find f(3x)

Solution:

f(x) = 4x + 4

f(3x) = 4(3x) + 4

= 12x + 4

Problem 9 :

When f(x) = -x - 1; Find f(x²)

Solution:

f(x) = -x - 1

f(x²) = -(x²) - 1

= -x² - 1