Hello there!
So, remember that m = the slope, and slope intercept form is represented as y = mx + b. To find the y intercept, place the values of x, y, and the slope into the equation.
The first step, ____ = (____)____ + b should look like 3 = (2/5)10 + b once you plug the values for your x and y values and slope.
The second step, ___ = ____ + b should look like 3 = 4 + b since you should multiply 2/5 x 10.
The final step, -1 = b should look like since you subtracted 4 from both sides of the equation.
Y = 2/5x - 1 is your final equation. I hope this helps, have a great rest of your day!
f(x)=x3−5
Replace f(x)
with y
.
y=x3−5
Interchange the variables.
x=y3−5
Solve for y
.
Since y
is on the right side of the equation, switch the sides so it is on the left side of the equation.
y3−5=x
Add 5
to both sides of the equation.
y3=5+x
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
y=3√5+x
Solve for y
and replace with f−1(x)
.
Replace the y
with f−1(x)
to show the final answer.
f−1(x)=3√5+x
Set up the composite result function.
f(g(x))
Evaluate f(g(x))
by substituting in the value of g into f
.
(3√5+x)3−5
Simplify each term.
Remove parentheses around 3√5+x
.
f(3√5+x)=3√5+x3−5
Rewrite 3√5+x3
as 5+x
.
f(3√5+x)=5+x−5
Simplify by subtracting numbers.
.
Subtract 5
from 5
.
f(3√5+x)=x+0
Add x
and 0
.
f(3√5+x)=x
Since f(g(x))=x
, f−1(x)=3√5+x is the inverse of f(x)=x3−5
.
f−1(x)=3√5+x
