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Review student working
The final answer is incorrect, but the expansion is useful. Seeing the working lets a teacher choose a more helpful next question.
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Example student · TMUA functions
The functions f and g are defined for all real x by f(x)=x2+1 and g(x)=2x−3. How many distinct real solutions are there to f(g(x))=g(f(x))?
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- Result
- Auto-checked: try again
- Submitted
- 16 Oct 2026, 13:00
- Help used
- 1 hints (reported by the practice screen)
Student answer
B. 1
Working
I expanded both compositions and obtained 2x² − 12x + 11 = 0. I chose one solution, but I am not sure how to count the roots.
Worked solution
(2x−3)2+1=2(x2+1)−3 gives
2x2−12x+11=0. Its discriminant is 56, so there are two real solutions.
Show an example teacher response
Your composition equation is correct. What does its discriminant tell you about the number of distinct real roots? Explain the connection before choosing again.
Illustrative feedback, not an actual teacher testimonial.