Question

Use the given information to find f(x + 1)
g(x) − f(x) = −2x + 5, g(x) = 5x − 3

Answer 1

`\mathbf{ f(x+1)=7x-1}`

Explanation:

We need to find f(x+1)

We are given:

`g(x) - f(x) = -2x + 5\:and\:g(x) = 5x -3`

First we need to find f(x)

By putting value of g(x) into g(x)-f(x)

`g(x) - f(x) = -2x + 5\\\Put\:value\:of\:g(x) = 5x -3\\5x-3-f(x)=-2x+5\\-f(x)=-2x+5-5x+3\\-f(x)=-2x-5x+5+3\\-f(x)=-7x+8\\f(x)=-(-7x+8)\\f(x)=7x-8\\`

We have,
`f(x)=7x-8`

Now finding f(x+1) by putting x=x+1

`f(x)=7x-8\\Put\:x=x+1\\f(x+1)=7(x+1)-8\\f(x+1)=7x+7-8\\f(x+1)=7x-1`

So,
`\mathbf{ f(x+1)=7x-1}`