10 f(x) = 4sin²x (a) Find f(23) Give your answer correct to 3 significant figures - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 3

First, we need to find g(34):

$g(x) = 2x - 3$

Substituting x = 34:

$g(34) = 2(34) - 3 = 68 - 3 = 65$

Now we will find f(g(34)): f(65):

$f(65) = 4sin²(65)$

Using a calculator, we calculate:

$sin(65) \approx 0.9063$

Thus,

$f(65) = 4(0.9063)² \approx 4(0.8214) \approx 3.2856$

Rounding this to three significant figures, we get:

3.29

The solution by Ivan is not fully correct because while he correctly set up the equation as (x + 4)² = 25, he did not adequately address both potential solutions.

The correct approach involves taking the square root of both sides, which yields:

$x + 4 = ±5$

Thus, we have two possible equations to solve:

1. $x + 4 = 5$
2. $x + 4 = -5$

The first equation gives:

$x = 5 - 4 = 1$

The second equation gives:

$x = -5 - 4 = -9$

Therefore, there are two solutions: x = 1 and x = -9. Ivan only considered one case and ignored the second solution.