What is the value of  (hog)(4), given that g(x)=sqrt x and h(x) = x^3 - 1?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the functions : g(x)=sqrt x and h(x) = x^3 - 1.

Now we are required to find hog(4).

hog(x) = h(g(x)) = h( sqrt x) = (sqrt x)^3 - 1.

Therefore hog(4)

=> (sqrt 4)^3 - 1

=> 2^3 - 1

=> 8 - 1

=> 7

The required value of hog(4) = 7.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

g(x) = (x)^(1/2). h(x) = x^3 - 1. To find hog(4).

We first find hog(x) .

h(x) = x^3 -1.

hog(x) = (g(x))^3 - 1.

hog(x) = (x^(1/2))^3 -1.

hog(x) = x^(3/2)-1 , as( x^m)^n = x^mn.

Now put x= 4 in hog(x) to get hog(4):

hog(4) = 4^(3/2) -1 = (4(1/2)^3 -1.

hog(4) = 2^3-1 = 8 - 1 = 7.

hog(4) = 7.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the value of (hog)(4), first, we'll have to determine the expression of (hog)(x).

(hog)(x) = h(g(x))

We'll substitute x by the expression of g(x), in the expression of h(x).

h(g(x)) = g(x)^3-1

But g(x) = sqrt x

h(g(x)) = (sqrt x)^3-1

h(g(x)) = x*sqrt x - 1

Now, we'll compute (hog)(4);

(hog)(4) = h(g(4))

We'll substitute x by 4 in the expression of h(g(x)):

h(g(4)) = 4*sqrt4 - 1

h(g(4)) = 4*2 - 1

h(g(4)) = 8 - 1

h(g(4)) = 7

So, the result of (hog)(4) = 7.

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