inverse. Help please?

[mrcl]

Find (f_og)^-1(x) if:

f(x) = √(x² + 4)
g(x) = 1/(x² - 2)

i've found :
f(g(x)) = f(1/(x² - 2))
y = √(1/(x² - 2)+4)
y² = 1/(x⁴-4x²+4) + 4(x⁴-4x²+4)/(x⁴-4x²+4)

and i stucked here cs i cant find the 'y'. it's 11th grade lesson.

 

[Deleted member 4993]

Find (f_og)^-1(x) if:

f(x) = √(x² + 4)
g(x) = 1/(x² - 2)

1) y = √(x² + 4) → switch 'x' and 'y' → x = √(y² + 4) → solve for 'y'

Please share your work with us.

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[mrcl]

1) y = √(x² + 4) → switch 'x' and 'y' → x = √(y² + 4) → solve for 'y'

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

okay sorry. i've changed it

 

[mmm4444bot]

f(x) = √(x² + 4)

g(x) = 1/(x² - 2)

f(g(x)) = f(1/(x² - 2))

y = √(1/(x² - 2)²+4)

y² = 1/(x⁴-4x²+4) + 4(x⁴-4x²+4)/(x⁴-4x²+4)

You forgot to type an exponent (shown above in red).

The last line is incorrect; squaring both sides gives:

y^2 = 1/(x^2 - 2)^2 + 4

As you're trying to solve for x, expanding (x^2-2)^2 is not needed. What's needed is to get x out of the denominator.

Try subtracting 4 from both sides.

Then, divide both sides by (y^2 - 4).

Next, multiply both sides by (x^2 - 2)^2.

See where that takes you. :cool: