Question

Uk thinks of a number.
He adds 5 to the number then multiplies the result by 7.
a) Write this as function using a mapping. (1)
The answer Jim gets is 91.
b) Use inverse functions to work out the number Jim thought of.
Show all your working

1
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Answer 1

Answer:

This is basic, I know, but I cannot seem to come up with the right answer.

Find the inverse of the function:

f(x)=3x+1

My steps: 1. Convert f(x) to y

y=3x+1

Switch places of x and y

x=3y+1

Try to solve for y. So I multiply the denominator by x to get rid of it

x(y+1)=3

After multiplying, I'm left with

xy+x=3

Which then converts to

2xy=3

Then I get rid of 2x on the left, placing it on the right

y=3−2x

Now I convert y to the inverse function

f−1(x)=3−2x

My answer is obviously wrong. The correct answer is:

f−1(x)=3−xx