Question

f(x) = 3x + 4 2f(x) 18f¹(x) simplifies to an integer. Work out this integer. You must show your working. Show your working +​

Answer 1

After calculating and simplifying the expression 2f(x) - 18f−1(x) with f(x) = 3x + 4, we find that it simplifies to the integer 32.

Step-by-step explanation:

We need to decipher the expression 2f(x) - 18f−1(x), where f(x) = 3x + 4. To find f−1(x), the inverse function of f(x), we must first switch x and y in the equation of f and solve for y. Thus, x = 3y + 4 becomes y = (x - 4) / 3. Now we can replace f(x) with its expression and f−1(x) with the inverse we calculated.

Let's simplify the given expression:

• 2f(x) = 2(3x + 4)
• 18f−1(x) = 18((x - 4) / 3)

Now calculate each part:

• 2f(x) = 2(3x + 4) = 6x + 8
• 18f−1(x) = 18((x - 4) / 3) = 6x - 24

Now subtract the two expressions:

• 2f(x) - 18f−1(x) = (6x + 8) - (6x - 24)
• 2f(x) - 18f−1(x) = 6x + 8 - 6x + 24
• 2f(x) - 18f−1(x) = 32

The simplified integer we get from the expression 2f(x) - 18f−1(x) is 32.