The functions f, g, and h are defined as follows. f(x) = -1...

The functions $f$, $g$, and $h$ are defined as follows. $f(x) = -1 + \sqrt{x - 2}$ $g(x) = -3 - |8 + x|$ $h(x) = \frac{3x^2 - 10}{x^2}$ Find $f(5)$, $g(2)$, and $h(4)$. Simplify your answers as much as possible. f(5) = g(2) = h(4) =

Transcript

00:01 In this question we have given here a function h x is equal to x squared plus 4 and divided by 5.

00:10 So we have to evaluate the function for the different values of x.

00:14 Okay, so what is given that? we have given here a number x and when we apply any rule on this given number such that squaring the number, then adding 4 and then whole term is divided by 5, that will give the result as the function hx okay so we can say that a function is a rule according to this concept and the function is representing by hx so hx is here the function at x now we have to find out the value of this function for the different values of x and the first one is two that means we have to put x is equal to to find out the value of function h2 so we will apply this rule to find out the value of h2 by putting x is equal to 2 so when we put x is equal to 2 in this function it will give the result as you can see here so it will be equal to 4 plus 4 that is 8 and it will be equal to 8 by 5 so this is the required value of h x at x is equal to 2 okay now coming to the next value that is minus 2 so we have to put x is equal to minus 2 in the given rule or we can say that in the value of x x here so when we put x is equal to minus 2 here so minus 2 square plus 4 upon 5.

01:36 So hence it will be equal to 8 by 5 again.

01:42 So this is the required value of hx at x is equal to minus 2.

01:47 Now we have to find out the value of hx at x is equal to 8.

01:52 So we have to put x is equal to a in this function and it will be equal to as a square plus 4 upon 5.

02:00 Okay and now what we have to do we have to put x is equal to minus x to find out the value of h minus x so when we put x is equal to minus x in this function like that minus x and then whole square plus four and divided by five so as you know that when power is even it will give the result in positive form so h minus x will be equal to x square plus 4 upon 5 that means we can say that it will be equal to the value of x okay now that means function is even the next value which is given here as a minus 2 that means we have to find out the value of function at x is equal to a minus 2 so it will be as a minus 2 and whole square plus 4 upon 5 now we have to simplify them...

Question

The functions $f$, $g$, and $h$ are defined as follows. $f(x) = -1 + \sqrt{x - 2}$ $g(x) = -3 - |8 + x|$ $h(x) = \frac{3x^2 - 10}{x^2}$ Find $f(5)$, $g(2)$, and $h(4)$. Simplify your answers as much as possible. f(5) = g(2) = h(4) =

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