If f(x) = 2x-3 and g(x) = x^2 -2 find fog(x) and gof(x).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We know that f(x) = 3x - 3 and g(x) = x^2 - 2. We need fog(x) and gof(x)

fog(x) = f(g(x))

=> f(x^2 - 2)

=> 2*(x^2 - 2) - 3

=> 2x^2 - 4 - 3

=> 2x^2 - 7

gof(x) = g(f(x))

=> g( 2x - 3)

=> (2x - 3)^2 - 2

=> 4x^2 + 9 - 12x - 2

=> 4x^2 - 12x + 7

This gives fog(x) = 2x^2 - 7 and gof(x) = 4x^2 - 12x + 7

hala718's profile pic

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

Posted on

f(x) = 2x-3

g(x) = x^2 -2

We need to find fog(x) and gof(x).

We know that fog(x) = f(g(x))

Then we will substitute with g(x) = x^2 -2

==> fog(x) = f( x^2 -2)

Now we will substitute with x = x^2-x in f(x).

==> fog(x) = 2(x^2-2) -3

We will open brackets.

==> fog(x) = 2x^2 -4 -3

==> fog(x) = 2x^2 -7

gof(x) = g(f(x)) = g(2x-3) = (2x-3)^2 -2 = 4x^2 -12x + 9 -2 = 4x^2 -12x +7

==> fog(x) = 2x^2 -7

==> gof(x) = 4x^2 -12x + 7

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