Question

For the function f(x) = 3x+2, find x such that f(x) = 14.

Answer 1

Simply use the fact that -
3x + 2 = 14

Answer 2

is that -3x or....

Answer 3

3x + 2 = 14
:)

Answer 4

is that it

Answer 5

Yep!
Were you looking for something complex ?? :P

Answer 6

YEA (0.0)

Answer 7

In that case, here we go -
Let there be a function g defined as
\[g(y) = f^{-1}(y)\]
Then
\[g(f(x)) = f^{-1}(f(x))=x\]

We were given that -
f(x) = 3x + 2
implies
\[x=\frac{ f(x) - 2 }{ 3 }\]
\[g(f(x)) = \frac{ f(x) - 2 }{ 3 }\]
\[g(y)=\frac{ y-2 }{ 3 }\]

The question said that
f(x) = 14
implies x = g(14)

Now can you find g(14) ?

Answer 8

Note that if f is not bijective; then g will not be a function in the first place.
Or in other words, we may not get a unique value of x satisfying f(x) = 14

Answer 9

so this inst the rite choice Given that f(x) = 14, we substitute 14 in to the equation in place of f(x)

14 = 3x + 2 Subtract two from both sides of the equation
12 = 3x Divide both sides of the equation by three.
4 = x
Answer: 4

Answer 10

"so this inst the rite choice"
IDK what does that mean..

Yea, you can (& should) simply solve 14 = 3x + 2

I only tried to justify this ^^ step using the concept of inverse of functions. ;)

Answer 11

srry (isn't) and thnx

Answer 12

You're welcome :)