If f(x) = 2x-3 and g(x) = x^2 -2 find fog(x) and gof(x).
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calendarEducator since 2010
write12,545 answers
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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
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
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