# Thread: couple of function problems

1. Given the function f(x)=2x^(5/2) :

Calculate exactly the value(s) of x when f(x)=6. If there is more than one such value, enter all possible values as a comma separated list of exact values. x=

If g(x)= 1/(t+7)-9
Solve g(t)=0. If there is more than one solution, enter all solutions as a comma separated list of exact values.

Whatever it is I'm doing is giving me the wrong answer

My working:

6= 2x^(5/2) is what is given for the first part, now how to i ISOLATE the x on the right side

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0= 1/(t+7) -9

9=1/(t+7) then would I multiply both sides by (t+7)

2. Originally Posted by midnightwynter
[snip]
0= 1/(t+7) -9

9=1/(t+7) then would I multiply both sides by (t+7)
Yes. Then expand and make t the subject.

3. Originally Posted by midnightwynter
Given the function f(x)=2x^(5/2) :
Calculate exactly the value(s) of x when f(x)=6. If there is more than one such value, enter all possible values as a comma separated list of exact values.

[snip]
My working:

6= 2x^(5/2) is what is given for the first part, now how to i ISOLATE the x on the right side

[snip]
Just take both sides to the power of $\displaystyle \frac{2}{5}$:

$\displaystyle 6 = (2x)^{\frac{5}{2}}$

$\displaystyle 6^{\frac{2}{5}} = 2x$

$\displaystyle \sqrt[5]{36} = 2x$

$\displaystyle x = \frac{\sqrt[5]{36}}{2}$.