Mathematics
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OpenStudy (anonymous):
Given: F(x) = 5x - 6 and G(x) = x - 4
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OpenStudy (anonymous):
i need help
OpenStudy (gorv):
what we need to do?????????
OpenStudy (anonymous):
find f*g inverse
OpenStudy (gorv):
f(g(x)) inverse
u mean????
OpenStudy (anonymous):
yes that
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OpenStudy (gorv):
or just we need to multiply them
OpenStudy (anonymous):
just multiply them
OpenStudy (anonymous):
Given: F(x) = 3x 2 + 1, G(x) = 2x - 3, H(x) = x
OpenStudy (gorv):
(5x-6)(x-6)=5x^2-6x-30x+36=5x^2-36x+36
OpenStudy (gorv):
let y=5x^2-36x+36
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OpenStudy (gorv):
now before doing inverse
OpenStudy (gorv):
f(x)=y=x^2+1
how we find inverse
OpenStudy (gorv):
just find value of x
y-1=x^2
(y-1)^1/2=x
now for inverse just switch x and y
OpenStudy (gorv):
y=(x-1)^1/2 is your inverse
OpenStudy (gorv):
do same for our prob
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OpenStudy (gorv):
find value of x
y=5x^2-36x+36
5x^2-36x+36=y
5x^2-36x+36-y=0
using quadratic formula\[\frac{ 36\pm \sqrt{36^2-4*5*(36-y)}}{ 10 }\]
OpenStudy (gorv):
that is the value of x
OpenStudy (gorv):
\[x=\frac{ 36\pm \sqrt{576+20y} }{ 10}\]
OpenStudy (gorv):
on switching
OpenStudy (gorv):
\[y=\frac{ 36\pm \sqrt{576+20x} }{ 10 }\]
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OpenStudy (gorv):
it is our inverse
OpenStudy (gorv):
similarly do for other
OpenStudy (gorv):
@quashia01