Help me please Find the inverse of the one-to-one function f(x) = 4x/3x + 4, and

Question

Help me please

Find the inverse of the one-to-one function f(x) = 4x/3x + 4, and verify that (f^-1 compfn f) (x) = x. Show that the function f(x) = 5x^2 + 12x + 4 is not one-to-one. Solve the right triangle given that beta = 45 degree and b = 5. The angle of elevation to the top of a pyramid is 37 degree. When 40 feet closer to the pyramid, the angle of elevation in 43 degree. What is the height of the pyramid? Determine the exact value of: sin(-840 degree) cot 11 n/4 Determine cos theta if csc theta = 1/4 and theta lies in the second quadrand. Find the inverse of the one-to-one function f(x) = 1/x - 1, and verify that (f^-1 compfn)(x) = x. For f(x) = 1 - 2x/x determine f(x + h) - f(x)/h Sketch the graph of: f(x) = -sin(1/2 x + x/2) + 1 For f(x) = -3x + 2 and g(x) = 1/x - 2 determine (g compfn f)(x) Evaluate: sin[cos^-1 (5/13) + tan -12/3] Determine the values of the remaining trigonometric functions of the acute angle theta, if cot theta = 7.

Explanation / Answer

Quiz3)

1)let f(x)=y

=>x=f-1(y)

given f(x)=4x/(3x+4)

4x/(3x+4)=y

(3x+4)/4x =1/y

(3/4)+(1/x)=1/y

(1/x)=(1/y)-(3/4)

(1/x)=(4-3y)/4y

x=4y/(4-3y)

f-1(y)=4y/(4-3y)

so f-1(x)=4x/(4-3x)

now

(f-1o f)(x)

=f-1(f(x))

=f-1(4x/(3x+4))

=4(4x/(3x+4))/[4-(3*4x/(3x+4))]

=(16x/(3x+4))/[(12x+16-12x)/(3x+4)]

=(16x/(3x+4))/[16/(3x+4)]

=x

2)given f(x)=5x2+12x+4

f(a)=f(b)

=>5a2+12a+4=5b2+12b+4

=>5a2-5b2+12a-12b=0

=>(5(a-b)(a+b))+(12(a-b))=0

=>(5(a+b)+12)(a-b)=0

=>(5(a+b)+12)=0

=>(a+b)=-12/5

=>ab when a=b -12/10

so f(x) is not one to one

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