Question

The function f is defined by f(x) = x^2-2x-24
if f (x + 3) = x^2+kx-21, what is the value of k?

Answer 1

Step-by-step explanation:

my guess it's 4

(x+7) (x-3)

Answer 2

The value of k for which f(x + 3) = x^2+kx-21 for the considered function f(x) is found to be k = 4

How to evaluate a given mathematical expression with variables if values of the variables are known?

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

It is given that:

$f(x) = x^2 -2x - 24$

and $f(x+3) = x^2 + kx - 21$

Putting x = x+3 in the definition of f(x), we get:

$f(x+3) = (x+3)^2 -2(x+3) -24\\\\f(x+3) = x^2 + 6x + 9 -2x -6 - 24\\\\f(x+3) = x^2 + 4x -21$

Comparing it with $f(x+3) = x^2 + kx - 21$, we see that k is having value as 4 for the considered function.

Thus, the value of k for which f(x + 3) = x^2+kx-21 for the considered function f(x) is found to be k = 4

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