Thread: Can someone show me how to solve these few problems step by step.

1. Given f(x)=x^2 and g(x)=(-7/x) find f(g(x)) and g(f(x))

2. Let f(x)=x+2 and g(x)= X^2-15, find f(g(4)) and g(f(4))

3. Let f(x)= (x-5/12), find f^-1(x)

4. Which of the following functions are one to one?
f(x)=|x+3|
g(x)=x^2
h(x)= sqrt(4-4x)
k(x)=x^3

Originally Posted by roxy6

1. Given f(x)=x^2 and g(x)=(-7/x) find f(g(x)) and g(f(x))

f[g(x)] = f(-7/x) = (-7/x)^2 = 49/x^2

g[f(x)] = g(x^2) = -7/x^2

2. Let f(x)=x+2 and g(x)= X^2-15, find f(g(4)) and g(f(4))

g(4) = 1 ... f(4) = 6

f[g(4)] = f(1) = 3

g[f(4)] = g(6) = 21

3. Let f(x)= (x-5/12), find f^-1(x)

y = (x-5)/12

swap x and y ...

x = (y-5)/12

12x = y-5

y = f^{-1}(x) = 12x + 5

4. Which of the following functions are one to one?
f(x)=|x+3|
g(x)=x^2
h(x)= sqrt(4-4x)
k(x)=x^3

first, you find out what one-to-one means ...

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