function and relAationsgiven g(x)=x^2+3 and h(x)=x-2 evaluate the composite function in: g[h(0)] h[g(0)] g[h(4)] h[g(-2)] g[h(x)] n[g(x)]

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to find equations of new functions g(h(x)) and h(g(x)) such that:

g(h(x)) = g(x-2) = (x-2)^2 + 3

Expanding the binomial yields:

g(h(x)) = x^2 - 4x + 7

h(g(x)) = h(x^2 + 3) = x^2 + 3 - 2 = x^2 + 1

You need to substitute 0 for x to find g(h(0)) such that:

g(h(0)) = 0^2 - 4*0 + 7 => g(h(0)) = 7

You need to substitute 4 for x to find g(h(4)) such that:

g(h(4)) = 4^2 - 4*4 + 7 => g(h(4)) = 7

You need to substitute 0 for x to find h(g(0)) such that:

h(g(0)) = 0^2 + 1 = 1

You need to substitute -2 for x to find h(g(-2)) such that:

h(g(-2)) = (-2)^2 + 1 = 5

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function g(x) = x^2 + 3 and h(x) = x - 2

g[h(0)] = g(-2) = 4 + 3 = 7

h[g(0)] = h(3) = 3 - 2 = 1

g[h(4)] = g(2) = 4 + 3 = 7

h[g(-2)] = h(7) = 7 - 2 = 5

g[h(x)] = g(x - 2) = (x - 2)^2 + 3 = x^2 - 4x + 4 + 3 = x^2 - 4x + 7

h[g(x)] = h(x^2 + 3) = x^2 + 3 - 2 = x^2 + 1

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