Let f(x) = 2x – 5 and g(x) = 7 – 2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Explanation:
Now
|f(x) + g(x)| = |f(x)| + |g(x)|
This is true only if both f(x) and g(x) are both negative or both positive or both are zero
Case 1: Now if both f(x) and g(x) are greater than or equal to zero.
f(x) = 2x - 5 ≥ 0 or x ≥ 52
g(x) = 7 - 2x ≥ 0 or x ≤ 72
∴52≤x≤72
Case 2: Now if both f(x) and g(x) are less than or equal to zero.
f(x) = 2x - 5 ≤ 0 or x ≤ 52
g(x) = 7 - 2x ≤ 0 or x ≥ 72
This means x ≥ 72 and x ≤ 52.
However, this is not possible.
Hence, option (d).
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