Question

Suppose that the function h is defined, for all real numbers, as follows.

Answer 1

The function h is defined, for all real numbers , answer is as follows -

h(1) = - 2

h(2) = 3

h(4) = 3.

function, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable

We have been given that

h(x) = 1/4(x) - 1       if x < -2

h(x) = -(x + 1)² + 2  if -2 ≤ x < 2

h(x) = 3                  if x ≥ 2

Find h (1), h (2), and h (4)

For h (1) -

Value of h(1) for h(x) = -(x + 1)² + 2 as if -2 ≤ x < 2

So put x = 1

h(x) = -(x + 1)² + 2

h(1) = -(1 + 1)² + 2

h(1) = -4 + 2

h(1) = - 2

For h (2) -

Value of h(2) for h(x) = 3 as  if x ≥ 2

h(x) = 3

h(2) = 3

For h (4) -

Value of h(4) for h(x) = 3 as  if x ≥ 2

h(x) = 3

h(4) = 3

Hence , the value for given functions - h(1) = - 2 , h(2) = 3 and h(4) = 3.

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