SOLUTION: Consider f(x) = 2x + 3. Find the inverse of this function. Verbally, compare what f does to x (“multiply by 2, then add 3”) to what f^-1 does to x.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Consider f(x) = 2x + 3. Find the inverse of this function. Verbally, compare what f does to x (“multiply by 2, then add 3”) to what f^-1 does to x.      Log On


   

Question 1140474: Consider f(x) = 2x + 3. Find the inverse of this function. Verbally, compare what f does to x (“multiply by 2, then add 3”) to what f^-1 does to x.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Inverse would be reverse of the steps done to x.
f:
multiplied by 2;
added 3.

inverse of f:
Starting with x,
subtract 3;
multiply by 1%2F2.
f%5E%28-1%29%28x%29=%28x-3%29%2F2

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+2x+%2B+3
to find inverse first replace f%28x%29 with y
y+=+2x+%2B+3.......swap x and y
x=+2y+%2B+3...........solve for y
x-3=+2y+

y=x%2F2-3%2F2+

=> f%5E-1%28x%29+=x%2F2-3%2F2+
compare:
what f does to x is: “multiply by 2, then add 3”
what f%5E-1 does to x is:"divide by 2, then subtract 3 divided by 2 ”