composition of functionscompose functions f(x)=x^2-16 and g(x)=x+2 then solve the equation fog=0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have the functions f(x)=x^2-16 and g(x)=x+2 and we need to solve fog(x)=0

fog(x) = 0

=>f(g(x)) = 0

=> f(x + 2) = 0

=> (x + 2)^2 - 16 = 0

=> (x + 2 - 4)(x + 2 + 4) = 0

=> (x - 2)(x + 6) = 0

=> x = 2 and x = -6

The required solutions are x = 2 and x = -6

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll have to compose the functions first:

(fog)(x) = f(g(x)) = f((x+2))

f((x+2)) = (x+2)^2 - 16

We'll notice that we have a difference of squares:

f((x+2)) = (x+2-4)(x+2+4)

f((x+2)) = (x-2)(x+6)

We'll solve the equation:

u(g(x))=0 if f(x)=x^2-16 and g(x)=x+2.

f((x+2)) = (x-2)(x+6) = 0

We'll set each factor as zero:

x-2 = 0

x = 2

x+6=0

x=-6

The solutions of the equation (fog)(x)=0 are {-6;2}.

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