Question

Please help with this question on functions?

Answer 1

See below

Explanation:

The way I interpret the question is that you have the function
`f(x)`, each with its own restricted domain.

Domain= the values `x` is allowed to take in the function.

The question really states, when translated into words that:

Given the function `f(x),` where if `x` is greater than 4, the function of `f` is equal to 3x-5. If instead `x` is less than or equal to 4 then a function of `x` is equal to `x^2`.

Thus;

1. If `x` is greater than 4, apply `f(x)=3x-5`
   2.If `x` is less than or equal to 4, apply `f(x)=x^2`

Hence in 1.:

`f(7)=3(7)-5=21-5=16`

For 2.:
`f(4)=4^2=16`

As the equation states that `f(x)=x^2` applies if `x` is less than OR equal to `4`.

For 3.: `4>x` as `x=-3` so we must apply the first function.

`f(-3)=(-3)^2=9`

Answer 2

1. 16
2. 16
3. 9

Explanation:

`f(7) =>` substitute `x=7` into `3x-5=21-5=16`
because `x>4`

`f(4) =>` substitute `x=4` into `x^2=4^2=16`
because `x=4`

`f(-3) =>` substitute `x=-3` into `x^2=(-3)^2=9`
because `x<4`