# Math Help - Functions Help.

1. ## Functions Help.

Hii (: I spend a couple of hours on these problems and I don't know how to solve them:

1. Show that if f is a constant function and g is any fucntion, then f of g and g of f are both constant functions.

2. Give an example of three functions f, g and h, none of which is a constant function, such that f of g = f of h but g is not equal to h.

I'm not sure if this is right but i did..
h(x)= x^2 , g(x)= x-3, and f(x)= √x
does that work? D:

3. Suppose f is a function whose domain equals to {2,4,7,8,9} and whose range equals to {-3,0,2,6,7}. Explain why f is a one to one function.

I don't understand what they mean by one to one function and the {2,4,7,8,9} thing. What does does it mean?

4. Give an example of a function f such that the domain of f and the range of f both equal the set of integers, but f is not a one to one function.

5. Explain why an even function whose domain contains a nonzero number cannot be a one-to-one function.

Thank you in advancee (: (: <3

2. Originally Posted by TeriyakiDonnQ
1. Show that if f is a constant function and g is any fucntion, then f of g and g of f are both constant functions.

For example, if:

$f:A\rightarrow B\;,g:B\rightarrow C\;,\;\quad f(x)=k\;(\forall x\in A)$

then

$(g\circ f)(x)=g[f(x)]=f(k)\quad (\forall x\in A)$

that is, $g\circ f$ is constant.

Fernando Revilla

3. Originally Posted by TeriyakiDonnQ
Hii (: I spend a couple of hours on these problems and I don't know how to solve them:

1. Show that if f is a constant function and g is any fucntion, then f of g and g of f are both constant functions.

2. Give an example of three functions f, g and h, none of which is a constant function, such that f of g = f of h but g is not equal to h.

I'm not sure if this is right but i did..
h(x)= x^2 , g(x)= x-3, and f(x)= √x
does that work? D:

3. Suppose f is a function whose domain equals to {2,4,7,8,9} and whose range equals to {-3,0,2,6,7}. Explain why f is a one to one function.

I don't understand what they mean by one to one function and the {2,4,7,8,9} thing. What does does it mean?

4. Give an example of a function f such that the domain of f and the range of f both equal the set of integers, but f is not a one to one function.

5. Explain why an even function whose domain contains a nonzero number cannot be a one-to-one function.

Thank you in advancee (: (: <3
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