2. Fungsi-fungsi f dan g ditentukan dengan rumus: \( \mathrm{f}(\mathrm{x})=\left(x^{\frac{1}{2}}-2\right)\left(x^{\frac{1}{2}}+2\right) \) dan \( \mathrm{g}(\mathrm{x})=(2 \mathrm{x}-3)^{2} \). Nilai \( (\mathrm{f}+\mathrm{g})(5) \) adalah ....
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Mari kita cari nilai \( (\mathrm{f}+\mathrm{g})(5) \) dengan terlebih dahulu menghitung \( \mathrm{f}(5) \) dan \( \mathrm{g}(5) \). Untuk fungsi \( \mathrm{f}(x) \): \[ \mathrm{f}(x) = \left(x^{\frac{1}{2}}-2\right)\left(x^{\frac{1}{2}}+2\right) \] kita substitusi \( x = 5 \): \[ \mathrm{f}(5) = \left(5^{\frac{1}{2}} - 2\right)\left(5^{\frac{1}{2}} + 2\right) = \left(\sqrt{5} - 2\right)\left(\sqrt{5} + 2\right) \] Menggunakan rumus \( (a-b)(a+b) = a^2 - b^2 \): \[ \mathrm{f}(5) = (\sqrt{5})^2 - 2^2 = 5 - 4 = 1 \] Sekarang untuk fungsi \( \mathrm{g}(x) \): \[ \mathrm{g}(x) = (2x - 3)^{2} \] kita substitusi \( x = 5 \): \[ \mathrm{g}(5) = (2(5) - 3)^{2} = (10 - 3)^{2} = 7^{2} = 49 \] Sekarang kita bisa menghitung \( (\mathrm{f}+\mathrm{g})(5) \): \[ (\mathrm{f}+\mathrm{g})(5) = \mathrm{f}(5) + \mathrm{g}(5) = 1 + 49 = 50 \] Jadi, nilai \( (\mathrm{f}+\mathrm{g})(5) \) adalah 50.
