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27.08.2020 •
Mathematics
4. What is the distance from point (-1, 4) to
the point (1, -1)?
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Ответ:
f(x)=x3−1f(x)=x3-1
Replace f(x)f(x) with yy.
y=x3−1y=x3-1
Interchange the variables.
x=y3−1x=y3-1
Solve for yy.
Move −1-1 to the right side of the equation by subtracting −1-1 from both sides of the equation.
y3=1+xy3=1+x
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
y=3√1+xy=1+x3
Reorder 11 and xx.
y=3√x+1y=x+13
Solve for yy and replace with f−1(x)f-1(x).
Replace the yy with f−1(x)f-1(x) to show the final answer.
f−1(x)=3√x+1f-1(x)=x+13
Set up the composite result function.
f(g(x))f(g(x))
Evaluate f(g(x))f(g(x)) by substituting in the value of gg into ff.
(3√x+1)3−1(x+13)3-1
Simplify each term.
f(3√x+1)=x+1−1f(x+13)=x+1-1
Simplify by subtracting numbers.
f(3√x+1)=xf(x+13)=x
Since f(g(x))=xf(g(x))=x, f−1(x)=3√x+1f-1(x)=x+13 is the inverse of f(x)=x3−1f(x)=x3-1.
f−1(x)=3√x+1
i hope this helped.