Algebra and Functions – Basic 1

(21) If \( f(x) = 2x – 1 \) and \( g(x) = x^2 + 3 \), find \( (f \circ g)(3) \) (i.e., \( f(g(3)) \)).

• (a) \( 9 \)
• (b) \( 16 \)
• (c) \( 13 \)
• (d) \( 12 \)

Answer

Correct Answer: (c) \( 13 \)

Find \( (f \circ g)(3) \) by first evaluating \( g(3) \) and then using this value in \( f(x) \). The detailed solution steps are: f(x) = 2x - 1, g(x) = x^2 + 3, f(g(3))

(22) Solve for \(x\):
\[ 3(2x + 1) = 5(x – 3) \]

• (a) \( x = -2 \)
• (b) \( x = 0 \)
• (c) \( x = 4 \)
• (d) \( x = 2 \)

Answer

Correct Answer: (c) \( x = 4 \)

To solve for \(x\), simplify and isolate \(x\) on one side of the equation. Here’s the step-by-step solution: 3(2x + 1) = 5(x - 3)

(23) Evaluate the expression:
\[ \frac{4x^2 – 9}{2x – 3} \]

• (a) \( 2x + 3 \)
• (b) \( 2x + 3 \)
• (c) \( 2x – 3 \)
• (d) \( 2x – 4 \)

Answer

Correct Answer: (b) \( 2x + 3 \)

To evaluate the expression, perform polynomial division. Here’s the step-by-step solution: \frac{4x^2 - 9}{2x - 3}

(24) If \( f(x) = 3x + 2 \) and \( g(x) = 2x – 1 \), find \( (g \circ f)(-2) \) (i.e., \( g(f(-2)) \)).

• (a) \( 1 \)
• (b) \( 7 \)
• (c) \( 5 \)
• (d) \( 3 \)

Answer

Correct Answer: (c) \( 5 \)

Find \( (g \circ f)(-2) \) by first evaluating \( f(-2) \) and then using this value in \( g(x) \). The detailed solution steps are: f(x) = 3x + 2, g(x) = 2x - 1, g(f(-2))

(25) Solve for \(x\):
\[ 4(2x – 1) = 2(3x + 2) \]

• (a) \( x = -1 \)
• (b) \( x = 1 \)
• (c) \( x = 6 \)
• (d) \( x = -2 \)

Answer

Correct Answer: (c) \( x = 6 \)

To solve for \(x\), simplify and isolate \(x\) on one side of the equation. Here’s the step-by-step solution: 4(2x - 1) = 2(3x + 2)