Question

Given: f(x) = x 2, g(x) = x + 6, h(x) = 7 Find h{g[f(x)] }. a. 7 b. 20 c. 55

Answer 1

Answer:

a. 7

Step-by-step explanation:

f(x) = x²

g(x) = x + 6

h(x) = 7

g[f(x)] = x² + 6

h{g[f(x)]} = 7

Answer 2

Given f(x) = x^2 + 1 and g(x) = x-2

a. Find (f-g)(-2)

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

[f-g](-2) = (-2)^2-(-2)+3 = 9

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b. Find f[g(5)]

f[g(5)] = f[5-2] = f[3] = 9+1 = 10

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problem a.

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(f-g)(x) = f(x) - g(x)

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(f-g)(-2) = f(-2) - g(-2)

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f(x) = x^2 + 1

f(-2) = (-2)^2 + 1

f(-2) = 4+1

f(-2) = 5

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g(x) = x-2

g(-2) = -2-2

g(-2) = -4

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f-g(-2) = f(-2) - g(-2) = 5 - (-4) = 5 + 4 = 9

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answer for a is:

f-g(-2) = 9

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problem b.

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g(x) = x-2

g(5) = 5-2

g(5) = 3

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f(x) = x^2 + 1

f(g(5)) = (g(5))^2 + 1

since g(5) = 3, equation becomes:

f(g(5)) = 3^2 + 1

f(g(5)) = 9 + 1 = 10

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answer for b is:

f(g(5)) = 10

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in general, you substitute whatever value is replacing x in the equation to get your answers.

looking at problem b in this way, we would get a general solution as follows:

f(x) = x^2 + 1

g(x) = x-2

substitute g(x) for x:

f(g(x)) = (g(x))^2 + 1

substitute the equation for g(x) on the right hand side.

f(g(x)) = (x-2)^2 + 1

remove parentheses:

f(g(x)) = x^2 - 4*x + 4 + 1

simplify:

f(g(x)) = x^2 - 4*x + 5

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substituting 5 for x:

f(g(5)) = (5^2 - 4*5 + 5

simplifying:

f(g(5)) = 25 - 20 + 5

f(g(5)) = 10

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answer is the same as above where we first solved for g(5) which became 3, and then substituted that value in f(g(x)) which made it f(3)).

Hope this helps!