Functions Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Functions questions. See exactly how to solve problems on function notation, evaluating functions, squaring, negatives.

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GCSE Higher70 questionsStep-by-step solutions
Question 1
1 markeasy
Given f(x)=2x+3f(x) = 2x + 3, work out f(4)f(4).

Worked solution

  1. Substitute x=4x = 4

    f(4)=2(4)+3f(4) = 2(4) + 3

    Replace every x in the rule with 4.

  2. Work out the arithmetic

    2(4)+3=8+32(4) + 3 = 8 + 3

    Multiply first, then add.

  3. State the value

    f(4)=11f(4) = 11

    So f(4)=11f(4) = 11.

Answer
f(4)=11f(4) = 11
Question 2
1 markeasy
Given f(x)=3x−5f(x) = 3x - 5, work out f(2)f(2).

Worked solution

  1. Substitute x=2x = 2

    f(2)=3(2)−5f(2) = 3(2) - 5

    Put 2 in place of x.

  2. Work it out

    3(2)−5=6−53(2) - 5 = 6 - 5

    3 times 2 is 6, then subtract 5.

  3. State the value

    f(2)=1f(2) = 1

    So f(2)=1f(2) = 1.

Answer
f(2)=1f(2) = 1
Question 3
1 markeasy
Given f(x)=x2f(x) = x^2, work out f(5)f(5).

Worked solution

  1. Substitute x=5x = 5

    f(5)=52f(5) = 5^2

    Replace x with 5 and square it.

  2. Square the number

    52=255^2 = 25

    5 times 5 is 25.

  3. State the value

    f(5)=25f(5) = 25

    So f(5)=25f(5) = 25.

Answer
f(5)=25f(5) = 25
Question 4
2 markseasy
Given f(x)=5xf(x) = 5x, work out f(−3)f(-3).

Worked solution

  1. Substitute x=−3x = -3

    f(−3)=5×(−3)f(-3) = 5 \times (-3)

    Be careful with the negative sign.

  2. Multiply

    5×(−3)=−155 \times (-3) = -15

    A positive times a negative is negative.

  3. State the value

    f(−3)=−15f(-3) = -15

    So f(−3)=−15f(-3) = -15.

Answer
f(−3)=−15f(-3) = -15
Question 5
1 markeasy
Given f(x)=2x+1f(x) = 2x + 1, work out f(0)f(0).

Worked solution

  1. Substitute x=0x = 0

    f(0)=2(0)+1f(0) = 2(0) + 1

    Anything multiplied by 0 is 0.

  2. Simplify

    2(0)+1=0+12(0) + 1 = 0 + 1

    The first term vanishes.

  3. State the value

    f(0)=1f(0) = 1

    So f(0)=1f(0) = 1.

Answer
f(0)=1f(0) = 1

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