# Math Functions Practice with Answer Key

**Practice Questions:**

**1. Find g○f if f(x) = 2x + 5 and g(x) = 5x + 2.**

A. 5x + 5

B. 10x + 27

C. 10x + 2

D. 25x + 25

E. 4x + 10

**2. If f(x) = 1 + x ^{2}, find f○f .**

A. 1 + x^{2 }+ x^{4}

B. 2 + x^{2 }+ x^{4}

C. 2 + x^{2}

D. 1 + x^{4}

**3. If f(x) = -x, g(x) = 2x + 1 and h(x) = x ^{2}, find f○g**○h .

A. x^{2} – 1

B. 2x^{2} – 1

C. x^{2 }– 2

D. x^{2} + 1

E. x^{2 }+ 2

**4. Which of the following functions have the largest domain?**

A. I

B. II

C. III

D. IV

**Answer Key**

**1. B. 10x + 27**

f(x) = 2x + 5

g(x) = 5x + 2.

g○f = g(f(x)) = g(2x + 5) = 5(2x + 5) + 2 = 10x + 25 + 2 = 10x + 27

**2. D. 2+2×2+x4**

f(x)=1+x2

f○f=f(f(x))=f(1+x2)=1+(1+x2)2=1+1+2×2+x4=2+2×2+x4

**3. B. -2x ^{2 }– 1**

f(x) = -x

g(x) = 2x + 1

h(x) = x

^{2}

f○g○h = f(g(h(x))) = f(g(x

^{2})) = f(2x

^{2 }+ 1) = -(2x

^{2 }+ 1) = -2x

^{2 }– 1

**3. C**

Without any restrictions, the domain of a function is (-∞, +∞). The restrictions are found by checking the denominator of the function. If there are any values that make the denominator zero; since division by zero is undefined, these x values should be eliminated from the domain:

f(x) = (x + 1) / (x – 2) : Notice that the denominator is x – 2 and x = 2 value makes it zero, so makes the function undefined. The domain of this function is (-∞, +∞) – {2}.

f(x) = (x + 7) / (x^{2} + 5x + 6) : Notice that the denominator is x^{2} + 5x + 6 which can be factorised as

(x + 2)(x + 3). Then, x = – 2 and x = – 3 values make the denominator zero, so make the function undefined. The domain of this function is (-∞, +∞) – {- 3, – 2}.

f(x) = (x^{2} – 9) / (x + 3) : Notice that first, it is possible to simplify the function:

f(x) = (x^{2} – 9) / (x + 3) = (x + 3)(x – 3) / (x + 3) = x – 3. Then, the denominator has vanished; the domain of this function is (-∞, +∞).

f(x) = (4x + 7) / (9x^{2} – 4) : Notice that the denominator is 9x^{2} – 4 which can be factorised as

(3x – 2)(3x + 2). It is not possible to simplify. Then, x = 2/3 and x = – 2/3 values make the denominator zero, so make the function undefined. The domain of this function is (-∞, +∞) – {- 2/3, 2/3}.

Function (x^{2} – 9) / (x + 3) has the largest domain.

The correct answer is **(C)**.