Home
Class 12
MATHS
Consider f:R+->[-9,oo[ given by f(x)=5x^...

Consider `f:R_+->[-9,oo[` given by `f(x)=5x^2+6x-9`. Prove that `f` is invertible with `f^(-1)(y)=(sqrt(54+5y)-3)/5`

Text Solution

Verified by Experts

`f(x)=5x^2+6x=9=y`
`5x^2+6x-(9+y)=0`
`x=(-6sqrt(6^2+20(a+y)))/10`
`x=(-6pmsqrt(226+20y))/10`
`x=(-3pmsqrt(54+54))/5`
`f:R^+->[-9,oo[`
x is positive for y`in[-9,oo]`
`x=(sqrt(54+54)-3)/5`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Consider f : R rarr (-9 ,oo) given by f(x) = 5x^(2)+ 6x-9 . Prove that f is invertible with f^(-1) (y) = ((sqrt(54+5y)-3)/(5)) where R^(+) is the set of all positive real numbers.

Consider f: R_+->[-5,oo) given by f(x)=9x^2+6x-5 . Show that f is invertible with f^(-1)(y)=(((sqrt(y+6))-1)/3)

Consider f:R rarr[-5,oo) given by f(x)=9x^(2)+6x-5. show that f is invertible with f^(-1)(y)=((sqrt(y+6)-1)/(3))

Consider f: R rarr [-5,oo) given by f(x)=9x^2+6x-5 . Show that f is invertible with f^(-1)(y)=((sqrt(y+6)-1)/3)dot

Consider f : R_+ rarr (-9, infty) given by f(x) = 5x^2 + 6x - 9 . Prove that f is invertible with f^-1 (y) = (sqrt(54+5y)-3)/(5)

Consider f: Rrarr[-5, oo] given by f(x) = 9x^2 + 6x - 5 . Show that f is invertible with f^(-1)(y)=[(sqrt(y+6)-1)/3]

Consider f:Rto[-5oo] given by f(x)9x^2+6x-5 , show that f is invertible with f^(-1)(y)={(sqrt(y+6))/3)}

Consider f:R_(+) to [-5, oo) given by f(x)=9x^(2)+6x-5 . Show that f is invertible with f^(-1)(y)= ((sqrt(y+6)-1)/(3)) . Hence. Find (i) f^(-1)(10)" " (ii) y" if "f^(-1)(y)=(4)/(3) where R_(+) is the set of all non-negative real numbers.