Question

@ABCD is a square and ABE is an equilateral
triangle on the side AB of the square. ZDAE
measures.​

Answer 1

Answer:

A function f : R ----> R defined by f(x)=\frac{3}{5}x+2f(x)=

5

3

x+2 , x\in Rx∈R

let's take x_1x

1

and x_2x

2

are two numbers in domain of given function such that, f(x_1)=f(x_2)f(x

1

)=f(x

2

)

or, \frac{3}{5}x_1+2=\frac{3}{5}x_2+2

5

3

x

1

+2=

5

3

x

2

+2

or, \frac{3}{5}x_1=\frac{3}{5}x_2

5

3

x

1

=

5

3

x

2

or, x_1=x_2x

1

=x

2

hence, f is one - one function.

we know, every function is an onto function only when co - domain = range.

here function ,f(x) = 3/5 x + 2 is a linear polynomial function. we know, every polynomial function is defined in all real numbers and range of polynomial function belongs to all real numbers.

given, co - domain belongs to R

so, range belongs to R

so, f is onto function.

now, f(x) = 3/5 x + 2

or, y = 3/5 x + 2

or, y - 2 = 3/5 x

or, x = 5(y - 2)/3

hence, f^{-1}=\frac{5(x-2)}{3}f

−1

=

3

5(x−2)