Question

Let g(x)= -3x and h(x) x^2+3 Find (g°h)(0)

Answer 1

Answer is   -9

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Work Shown:

(g°h)(x) is the same as g(h(x))

So, (g°h)(0) = g(h(0))

Effectively h(x) is the input to g(x). Let's first find h(0)

h(x) = x^2+3

h(0) = 0^2+3

h(0) = 3

So g(h(x)) becomes g(h(0)) after we replace x with 0, then it updates to g(3) when we replace h(0) with 3.

Now let's find g(3)

g(x) = -3x

g(3) = -3*3

g(3) = -9

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alternatively, you can plug h(x) algebraically into the g(x) function

g(x) = -3x

g( h(x) ) = -3*( h(x) ) ... replace all x terms with h(x)

g( h(x) ) = -3*(x^2 + 3) ... replace h(x) on right side with x^2+3

g( h(x) ) = -3x^2 - 9

Next we can plug in x = 0

g( h(0) )  = -3(0)^2 - 9

g( h(0) ) = -9

we get the same result.