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If \(f(x)=4\) and \(g(x)=x^2-1\), what is \((f-g)(x)\)?यदि \(f(x)=4\) और \(g(x)=x^2-1\) हों, तो \((f-g)(x)\) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(5-x^2\)\(5-x^2\)
By the definition of the difference of two functions, \((f-g)(x)=f(x)-g(x)\). Hence, \((f-g)(x)=4-(x^2-1)=4-x^2+1=5-x^2\). The brackets are important because the minus sign changes the signs inside \(g(x)\). Exam tip: in \(f-g\), subtract the second function from the first.दो फलनों के अंतर की परिभाषा के अनुसार \((f-g)(x)=f(x)-g(x)\)। इसलिए \((f-g)(x)=4-(x^2-1)=4-x^2+1=5-x^2\)। ऋण चिह्न के कारण पूरे \(g(x)\) को घटाते समय कोष्ठक का ध्यान रखें। परीक्षा-युक्ति: \(f-g\) में पहले फलन में से दूसरे फलन को घटाया जाता है।
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