Question

Okay, I know the answer is 50 but I am so confused as to why I can’t figure it out please help

Answer 1

K. 50

Explanation:

Given functions:

`\begin{cases}f(x)=x^2-5x+6\\g(x)=x^2-7x-10\end{cases}`

To calculate g(f(-1)), we first need to evaluate f(-1) and then use the result as the input for function g(x).

To calculate f(-1), substitute x = -1 into f(x):

`\begin{aligned}f(-1)&=(-1)^2-5(-1)+6\\&=1+5+6\\&=6+6\\&=12\end{aligned}`

Now that we have the value of f(-1), we can use it as the input for the function g(x).

`\begin{aligned}g(12)&=(12)^2-7(12)-10\\&=144-84-10\\&=60-10\\&=50\end{aligned}`

Therefore, g(f(-1)) = 50.

Answer 2

Option (K), 50

Explanation:

To find g(f(-1)), we first need to evaluate f(-1) and then plug that value into g(x).

(1) - Evaluating f(-1):

We start by substituting x = -1 into the expression for f(x):

f(x) = x² - 5x + 6

⇒ f(-1) = (-1)² - 5(-1) + 6

⇒ f(-1) = 1 + 5 + 6

∴ f(-1) = 12

So, f(-1) = 12.

(2) - Evaluating g(f(-1)):

Now that we have the value of f(-1), we substitute this value into the expression for g(x):

g(x) = x² - 7x - 10

⇒ g(f(-1)) = (f(-1))² - 7f(-1) - 10

⇒ g(f(-1)) = (12)² - 7(12) - 10

⇒ g(f(-1)) = 144 - 84 - 10

∴ g(f(-1)) = 50

Thus, the correct option is (K), 50.

`\hrulefill`

Additional Information:

Function Composition: In this problem, we used the concept of function composition. When we have two functions, f(x) and g(x), we can create a new function by "plugging in" one function into another. In this case, g(f(-1)) means we're first finding the value of f(-1) and then using that result as the input for the function g(x).

Evaluating a Function: To evaluate a function at a particular value of x, we simply substitute that value for x in the function expression and perform the calculations.

Quadratic Function: The functions f(x) and g(x) are both quadratic functions since they have the form ax² + bx + c, where a, b, and c are constants. Quadratic functions have a parabolic shape when graphed.