Question

Given f z please help

Answer 1

Answer:

z = -11, z = -2

Step-by-step explanation:

Given that, ($f(z)=\sqrt{z+27} -z$) 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.

$f(z)=\sqrt{z+27}-z=7$

Use inverse operations to solve,

$\sqrt{z+27}-z=7\\\\\sqrt{z-27}=7+z\\\\z+27 = (7+z)^2\\\\z + 27 = 49+14z+z^2\\ -(27+z)\\\\0 = z^2+13z+22$

Factor,

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

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

$z=-11,z=-2$

Answer 2

Answer:

Then solve the rest using the quadratic formula