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# Write the equation of the inverse: So Many Math Questions...?

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Write the equation of the inverse: Apr 20, 2019

#1
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Solve each equation for 'x' ....then switch the 'x' and 'y'....

I'll do the third one....you try the other two

y = sqrt(5x-6)     square both sides

y^2 = 5x-6          add 6 to both sides

y^2 + 6 = 5x       divide both sides by 5

(y^2+6)/5 = x      now swithch the 'x's and 'y's

y = (x^2+6) / 5    done!

Apr 20, 2019
#2
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a)    y = x^2 + 3     subtract 3 from both sides

y - 3  = x^2     take both roots

±√ [ y - 3 ]  =  x           "swap"  x and y

±√[ x - 3]  =  y   Note, GM.....this is the inverse.....but  not an inverse "function".....since the original function isn't one-to-one.....then we don't have a true inverse function

b)  y = [ (1/4)x + 6 ] ^3    take the cube root of both sides

∛y  = (1/4)x + 6             subtract 6 from both sides

∛[y]  - 6   =  (1/4) x         multiply through by 4

4 ∛[y]  - 24   =  x             swap x and y

4 ∛[x] - 24  = y  =    the inverse   Apr 21, 2019