If f(x)=5x-2 and g(x)= cubed sqrt of x ( or x^(1/3)), evaluate (fog)(-8)

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have f(x) = 5x - 2 and g(x) = x^(1/3) [ I have assumed by cubed sqrt you mean raised to the power (1/3)]

We have to find fog( - 8)

fog(x) = f(g(x)) = f( x^(1/3))

=5 * x^(1/3) - 2

For x = -8

fog(-8) = 5*(-8)^(1/3) - 2

=> 5* (-2) - 2

=> -10 - 2

=> -12

The required result is -12

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that: f(x) = 5x-2. g(x) = (x^1/30 We need to find fog(x) First we will rewrite fog(x) as follows: fog(x) = f(g(x)) We will substitute with g(x) = x^1/3 ==> fog(x) = f(x^1/3) Now we will substitute with x^1/3 in f(x) ==> fog(x) = 5(x^1/3) -2 Now we will substitute with x=-8. ==> fog(x) = 5(-8^1/3) -2 = 5*-2 -2 = -10 -2 = -12 ==> fog(-8) = -12.

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