## Fill-in-the-blank proofs
for Section 4.3

**Claim:**
The function *f* : **(0, ∞)**
→ **(5, ∞)** with rule *f*(*x*) = 3*x*
+ 5 is onto.

*Proof*.* *Click here.

**Claim:**
The function *f* : **N**
→ **Q** with rule *f*(*x*) = 2/(*x*
+ 1) is one-to-one.

*Proof*.* *Click here.**
**

** Claim:**
If the function *f* : **Q**
→ **Q** is onto, then the function *g* : **Q**→
**Q** with rule *g*(*x*) = *f*(2*x*)
is onto.

* Proof*.* *Click here.

**Claim:**
If the function *f* : **Z
**→ **Z** is one-to-one, then the function *h*
: **Z **→
**Z** with rule *h*(*x*) = *f*(2*x*)
is one-to-one.

* Proof*.* *Click here.