if f(x)=x^2-4x and g(x)=2x+3, express (fog)(x) in simpliest form?

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hala718's profile pic

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

Posted on

f(x) = x^2 - 4x

g(x) = 2x+3

We need to find the equation of fog(x).

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

We will substitute with g(x) = 2x+3

==> f(g(x)) = f( 2x+3)

Now we will substitute with x= 2x+3 into f(x).

==> f(g(x)) = g(x)^2 - 4g(x)

                   = (2x+3)^2 - 4(2x+3)

                    = 4x^2 + 12x + 9 - 8x - 12

Now we will combine like terms.

==> f(g(x)) = 4x^2 +4x - 3

Then fog(x) = 4x^2 + 4x -3 .

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The functions we have are f(x) = x^2 - 4x and g(x) = 2x + 3.

(fog)(x) is to be found in the simplest form.

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

g(x) = 2x + 3

=> f(2x + 3)

f(x) = x^2 - 4x

=> (2x + 3)^2 - 4*(2x + 3)

=> 4x^2 + 12x + 9 - 8x - 12

=> 4x^2 + 4x - 3

(fog)(x) in the simplest form is 4x^2 + 4x - 3

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The function f(x)=x^2-4x and g(x)=2x+3.

(fog)(x)

= f(g(x))

Substitute g(x) with 2x+3

= f(2x+3)

= (2x+3)^2 - 4(2x+3)

= 4x^2 + 9 + 12x - 8x - 12

= 4x^2 + 4x - 3

The expression for fog(x) is 4x^2 + 4x - 3

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