Question

Given the function

` f(x)= {( -6, x<0), ( sqrt(7 x^2 + 9), x\geq 0):}`
Calculate the following values:
`f(-6)= ` `f(0)= ` `f(6)= `

Answer 1

f(-6) = -6 (since -6 is less than 0)

f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)

f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)

Explanation:

To evaluate the function at different values of x, we need to use the appropriate formula depending on whether x is less than 0 or greater than or equal to 0.

For x less than 0:

f(x) = -6 (since the function is defined as f(x) = -6 for x < 0)

For x greater than or equal to 0:

f(x) = sqrt(7x^2 + 9)

Therefore:

f(-6) = -6 (since -6 is less than 0)

f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)

f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)