Question

Given f z please help

Answer 1

Then solve the rest using the quadratic formula

Answer 2

z = -11, z = -2

Explanation:

Given that, (
`f(z)=√(z+27) -z`) and (
`f(z)=7`), set up an equation that puts the first value of (
`f(z)`) equal to the other given value of the function.

`f(z)=√(z+27)-z=7`

Use inverse operations to solve,

`√(z+27)-z=7\\\\√(z-27)=7+z\\\\z+27 = (7+z)^2\\\\z + 27 = 49+14z+z^2\\ -(27+z)\\\\0 = z^2+13z+22`

Factor,

`0=(z+11)(z+2)`

Solve using the zero product property, the zero product property states that any number times zero equals zero;

`z=-11,z=-2`